Problem: Express this product in scientific notation: $(9.70\times 10^{2})\times (8.00\times 10^{-2})$
Answer: Start by collecting like terms together. $= (9.70\times 8.00) \times (10^{2}\times 10^{-2})$ When multiplying exponents with the same base, add the powers together. $= 77.6 \times 10^{2\,+\,-2}$ $= 77.6 \times 10^{0}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $77.6$ is the same as $7.760 \times 10$ $ = {7.760 \times 10} \times 10^{0} $ $= 7.760\times 10^{1}$